MinT - Best Known (23, 23+75, s)-Nets in Base 7

Best Known (23, 23+75, s)-Nets in Base 7

(23, 23+75, 30)-Net over F₇ — Constructive and digital

Digital (23, 98, 30)-net over F₇, using

net from sequence [i] based on digital (23, 29)-sequence over F₇, using
- Niederreiter sequence [i]

(23, 23+75, 72)-Net over F₇ — Digital

Digital (23, 98, 72)-net over F₇, using

t-expansion [i] based on digital (22, 98, 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]

(23, 23+75, 377)-Net in Base 7 — Upper bound on s

There is no (23, 98, 378)-net in base 7, because

1 times m-reduction [i] would yield (23, 97, 378)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 9949 410169 074345 213161 916220 433811 730046 676821 320643 077143 254137 336040 988428 513749 > 7⁹⁷ [i]