MinT - Best Known (23, 113, s)-Nets in Base 16

Best Known (23, 113, s)-Nets in Base 16

(23, 113, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 113, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 113, 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, 113, 129)-Net over F₁₆ — Digital

Digital (23, 113, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 113, 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, 113, 1216)-Net in Base 16 — Upper bound on s

There is no (23, 113, 1217)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12017 590811 073658 229359 890466 549689 257661 687298 737369 985465 367419 115312 666680 693534 567536 490711 365548 423920 697884 810068 963804 912901 110976 > 16¹¹³ [i]