MinT - Best Known (23, 23+76, s)-Nets in Base 16

Best Known (23, 23+76, s)-Nets in Base 16

(23, 23+76, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 99, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 99, 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]

(23, 23+76, 129)-Net over F₁₆ — Digital

Digital (23, 99, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 99, 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]

(23, 23+76, 1352)-Net in Base 16 — Upper bound on s

There is no (23, 99, 1353)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 164393 716490 541324 304600 740741 597260 187563 634223 454105 064081 261207 831181 737885 222562 076741 092282 144745 614976 623557 912136 > 16⁹⁹ [i]