MinT - Best Known (34−28, 34, s)-Nets in Base 7

Best Known (34−28, 34, s)-Nets in Base 7

(34−28, 34, 14)-Net over F₇ — Constructive and digital

Digital (6, 34, 14)-net over F₇, using

net from sequence [i] based on digital (6, 13)-sequence over F₇, using
- Niederreiter sequence [i]

(34−28, 34, 24)-Net over F₇ — Digital

Digital (6, 34, 24)-net over F₇, using

t-expansion [i] based on digital (4, 34, 24)-net over F₇, using
- net from sequence [i] based on digital (4, 23)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 4 and N(F) ≥ 24, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(34−28, 34, 99)-Net in Base 7 — Upper bound on s

There is no (6, 34, 100)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7³⁴, 100, S₇, 28), but
- the linear programming bound shows that MÂ â‰¥ 1278 094337 222159 317664 503843 706974 145627 541045 963486 591902 / 23059 219539 901402 418336 736749 > 7³⁴ [i]