MinT - Best Known (99−37, 99, s)-Nets in Base 4

Best Known (99−37, 99, s)-Nets in Base 4

(99−37, 99, 130)-Net over F₄ — Constructive and digital

Digital (62, 99, 130)-net over F₄, using

13 times m-reduction [i] based on digital (62, 112, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 56, 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]

(99−37, 99, 204)-Net over F₄ — Digital

Digital (62, 99, 204)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−37, 99, 4759)-Net in Base 4 — Upper bound on s

There is no (62, 99, 4760)-net in base 4, because

1 times m-reduction [i] would yield (62, 98, 4760)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 100580 972818 936905 056356 368663 936675 534280 530139 621351 497673 > 4⁹⁸ [i]