MinT - Best Known (78−44, 78, s)-Nets in Base 9

Best Known (78−44, 78, s)-Nets in Base 9

(78−44, 78, 81)-Net over F₉ — Constructive and digital

Digital (34, 78, 81)-net over F₉, using

t-expansion [i] based on digital (32, 78, 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]

(78−44, 78, 84)-Net in Base 9 — Constructive

(34, 78, 84)-net in base 9, using

base change [i] based on digital (8, 52, 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]

(78−44, 78, 128)-Net over F₉ — Digital

Digital (34, 78, 128)-net over F₉, using

t-expansion [i] based on digital (33, 78, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(78−44, 78, 2721)-Net in Base 9 — Upper bound on s

There is no (34, 78, 2722)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 269 824044 918882 217270 076660 054294 708232 752094 434546 793734 149926 381243 664545 > 9⁷⁸ [i]