MinT - Best Known (97−64, 97, s)-Nets in Base 7

Best Known (97−64, 97, s)-Nets in Base 7

(97−64, 97, 35)-Net over F₇ — Constructive and digital

Digital (33, 97, 35)-net over F₇, using

net from sequence [i] based on digital (33, 34)-sequence over F₇, using
- Niederreiter sequence [i]

(97−64, 97, 96)-Net over F₇ — Digital

Digital (33, 97, 96)-net over F₇, using

net from sequence [i] based on digital (33, 95)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 33 and N(F) ≥ 96, using
  - an algebraic function field by Teo [i]

(97−64, 97, 756)-Net in Base 7 — Upper bound on s

There is no (33, 97, 757)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 9680 091833 937865 949832 459631 228656 457679 564432 521403 450683 807484 360860 720353 603073 > 7⁹⁷ [i]