MinT - Best Known (78−26, 78, s)-Nets in Base 3

Best Known (78−26, 78, s)-Nets in Base 3

(78−26, 78, 128)-Net over F₃ — Constructive and digital

Digital (52, 78, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 39, 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]

(78−26, 78, 149)-Net over F₃ — Digital

Digital (52, 78, 149)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−26, 78, 2053)-Net in Base 3 — Upper bound on s

There is no (52, 78, 2054)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 484797 903120 526994 384461 546068 903125 > 3⁷⁸ [i]