MinT - Best Known (97−63, 97, s)-Nets in Base 7

Best Known (97−63, 97, s)-Nets in Base 7

(97−63, 97, 35)-Net over F₇ — Constructive and digital

Digital (34, 97, 35)-net over F₇, using

t-expansion [i] based on digital (33, 97, 35)-net over F₇, using
- net from sequence [i] based on digital (33, 34)-sequence over F₇, using
  - Niederreiter sequence [i]

(97−63, 97, 96)-Net over F₇ — Digital

Digital (34, 97, 96)-net over F₇, using

t-expansion [i] based on 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]

(97−63, 97, 836)-Net in Base 7 — Upper bound on s

There is no (34, 97, 837)-net in base 7, because

1 times m-reduction [i] would yield (34, 96, 837)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1349 971312 971299 674450 807270 872126 432372 485599 133726 070658 414628 021085 461493 158935 > 7⁹⁶ [i]