MinT - Best Known (108−64, 108, s)-Nets in Base 9

Best Known (108−64, 108, s)-Nets in Base 9

(108−64, 108, 81)-Net over F₉ — Constructive and digital

Digital (44, 108, 81)-net over F₉, using

t-expansion [i] based on digital (32, 108, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(108−64, 108, 84)-Net in Base 9 — Constructive

(44, 108, 84)-net in base 9, using

base change [i] based on digital (8, 72, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(108−64, 108, 147)-Net over F₉ — Digital

Digital (44, 108, 147)-net over F₉, using

t-expansion [i] based on digital (43, 108, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(108−64, 108, 2637)-Net in Base 9 — Upper bound on s

There is no (44, 108, 2638)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11 524765 044155 706234 206211 399626 059258 990343 625070 125070 457952 275671 083403 179559 486846 807843 724181 154305 > 9¹⁰⁸ [i]