MinT - Best Known (98−73, 98, s)-Nets in Base 7

Best Known (98−73, 98, s)-Nets in Base 7

(98−73, 98, 31)-Net over F₇ — Constructive and digital

Digital (25, 98, 31)-net over F₇, using

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

(98−73, 98, 72)-Net over F₇ — Digital

Digital (25, 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]

(98−73, 98, 427)-Net in Base 7 — Upper bound on s

There is no (25, 98, 428)-net in base 7, because

1 times m-reduction [i] would yield (25, 97, 428)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 9938 923334 062415 843301 044097 618574 830415 988311 468413 575591 010100 040211 657752 791489 > 7⁹⁷ [i]