MinT - Best Known (113−64, 113, s)-Nets in Base 9

Best Known (113−64, 113, s)-Nets in Base 9

(113−64, 113, 94)-Net over F₉ — Constructive and digital

Digital (49, 113, 94)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (4, 36, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]
2. digital (13, 77, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(113−64, 113, 96)-Net in Base 9 — Constructive

(49, 113, 96)-net in base 9, using

1 times m-reduction [i] based on (49, 114, 96)-net in base 9, using
- base change [i] based on digital (11, 76, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(113−64, 113, 168)-Net over F₉ — Digital

Digital (49, 113, 168)-net over F₉, using

net from sequence [i] based on digital (49, 167)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 49 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(113−64, 113, 3725)-Net in Base 9 — Upper bound on s

There is no (49, 113, 3726)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 677501 696492 004046 537330 245575 794708 075335 255804 219864 051079 624257 724216 121146 853761 651295 538149 386361 399809 > 9¹¹³ [i]