MinT - Best Known (98−45, 98, s)-Nets in Base 4

Best Known (98−45, 98, s)-Nets in Base 4

(98−45, 98, 90)-Net over F₄ — Constructive and digital

Digital (53, 98, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 49, 45)-net over F₁₆, using
- net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]

(98−45, 98, 103)-Net over F₄ — Digital

Digital (53, 98, 103)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(98−45, 98, 1344)-Net in Base 4 — Upper bound on s

There is no (53, 98, 1345)-net in base 4, because

1 times m-reduction [i] would yield (53, 97, 1345)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 25293 793968 735233 481278 425525 474772 688645 832883 053857 644704 > 4⁹⁷ [i]