MinT - Best Known (35−29, 35, s)-Nets in Base 7

Best Known (35−29, 35, s)-Nets in Base 7

(35−29, 35, 14)-Net over F₇ — Constructive and digital

Digital (6, 35, 14)-net over F₇, using

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

(35−29, 35, 24)-Net over F₇ — Digital

Digital (6, 35, 24)-net over F₇, using

t-expansion [i] based on digital (4, 35, 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]

(35−29, 35, 97)-Net in Base 7 — Upper bound on s

There is no (6, 35, 98)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7³⁵, 98, S₇, 29), but
- the linear programming bound shows that MÂ â‰¥ 12 620908 470515 985307 711925 285436 611586 040418 643890 425594 358250 / 32 907173 390876 495796 723290 378977 > 7³⁵ [i]