MinT - Best Known (88−67, 88, s)-Nets in Base 16

Best Known (88−67, 88, s)-Nets in Base 16

(88−67, 88, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 88, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 88, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(88−67, 88, 129)-Net over F₁₆ — Digital

Digital (21, 88, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 88, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(88−67, 88, 1293)-Net in Base 16 — Upper bound on s

There is no (21, 88, 1294)-net in base 16, because

1 times m-reduction [i] would yield (21, 87, 1294)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 582 961443 322698 608127 806322 762494 069362 978945 797589 464361 969586 822262 009086 597527 646586 256438 365084 575656 > 16⁸⁷ [i]