MinT - Best Known (26, 105, s)-Nets in Base 7

Best Known (26, 105, s)-Nets in Base 7

(26, 105, 31)-Net over F₇ — Constructive and digital

Digital (26, 105, 31)-net over F₇, using

t-expansion [i] based on digital (25, 105, 31)-net over F₇, using
- net from sequence [i] based on digital (25, 30)-sequence over F₇, using
  - Niederreiter sequence [i]

(26, 105, 72)-Net over F₇ — Digital

Digital (26, 105, 72)-net over F₇, using

t-expansion [i] based on digital (22, 105, 72)-net over F₇, using
- net from sequence [i] based on digital (22, 71)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 22 and N(F) ≥ 72, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(26, 105, 435)-Net in Base 7 — Upper bound on s

There is no (26, 105, 436)-net in base 7, because

1 times m-reduction [i] would yield (26, 104, 436)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 8411 660164 534660 241626 513832 130528 512546 867014 897377 607664 817911 192610 554407 201798 585057 > 7¹⁰⁴ [i]