MinT - Best Known (26, 26+81, s)-Nets in Base 7

Best Known (26, 26+81, s)-Nets in Base 7

(26, 26+81, 31)-Net over F₇ — Constructive and digital

Digital (26, 107, 31)-net over F₇, using

t-expansion [i] based on digital (25, 107, 31)-net over F₇, using
- net from sequence [i] based on digital (25, 30)-sequence over F₇, using
  - Niederreiter sequence [i]

(26, 26+81, 72)-Net over F₇ — Digital

Digital (26, 107, 72)-net over F₇, using

t-expansion [i] based on digital (22, 107, 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, 26+81, 430)-Net in Base 7 — Upper bound on s

There is no (26, 107, 431)-net in base 7, because

1 times m-reduction [i] would yield (26, 106, 431)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 397795 256461 572086 274622 663147 536106 942175 273673 220108 427211 245105 104170 214595 838043 916305 > 7¹⁰⁶ [i]