MinT - Best Known (28, 68, s)-Nets in Base 7

Best Known (28, 68, s)-Nets in Base 7

(28, 68, 32)-Net over F₇ — Constructive and digital

Digital (28, 68, 32)-net over F₇, using

t-expansion [i] based on digital (27, 68, 32)-net over F₇, using
- net from sequence [i] based on digital (27, 31)-sequence over F₇, using
  - Niederreiter sequence [i]

(28, 68, 78)-Net over F₇ — Digital

Digital (28, 68, 78)-net over F₇, using

t-expansion [i] based on digital (27, 68, 78)-net over F₇, using
- net from sequence [i] based on digital (27, 77)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 27 and N(F) ≥ 78, using
    - an algebraic function field by Teo [i]

(28, 68, 1021)-Net in Base 7 — Upper bound on s

There is no (28, 68, 1022)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2977 668447 608211 994558 355141 628816 181517 109885 688107 178441 > 7⁶⁸ [i]