MinT - Best Known (93, 93+129, s)-Nets in Base 3

Best Known (93, 93+129, s)-Nets in Base 3

(93, 93+129, 64)-Net over F₃ — Constructive and digital

Digital (93, 222, 64)-net over F₃, using

t-expansion [i] based on digital (89, 222, 64)-net over F₃, using
- net from sequence [i] based on digital (89, 63)-sequence over F₃, using
  - base reduction for sequences [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]

(93, 93+129, 96)-Net over F₃ — Digital

Digital (93, 222, 96)-net over F₃, using

t-expansion [i] based on digital (89, 222, 96)-net over F₃, using
- net from sequence [i] based on digital (89, 95)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(93, 93+129, 487)-Net in Base 3 — Upper bound on s

There is no (93, 222, 488)-net in base 3, because

1 times m-reduction [i] would yield (93, 221, 488)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2991 304901 414613 287090 717201 209082 656528 946329 407087 434100 994512 690679 499519 947597 358090 456338 099343 532033 > 3²²¹ [i]