MinT - Best Known (49, 88, s)-Nets in Base 4

Best Known (49, 88, s)-Nets in Base 4

(49, 88, 98)-Net over F₄ — Constructive and digital

Digital (49, 88, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 44, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(49, 88, 106)-Net over F₄ — Digital

Digital (49, 88, 106)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 88, 1494)-Net in Base 4 — Upper bound on s

There is no (49, 88, 1495)-net in base 4, because

1 times m-reduction [i] would yield (49, 87, 1495)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 24113 767214 544981 877581 645825 636746 563648 641744 735952 > 4⁸⁷ [i]