MinT - Best Known (163−48, 163, s)-Nets in Base 4

Best Known (163−48, 163, s)-Nets in Base 4

(163−48, 163, 384)-Net over F₄ — Constructive and digital

Digital (115, 163, 384)-net over F₄, using

2 times m-reduction [i] based on digital (115, 165, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 55, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(163−48, 163, 759)-Net over F₄ — Digital

Digital (115, 163, 759)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−48, 163, 40088)-Net in Base 4 — Upper bound on s

There is no (115, 163, 40089)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 136 734334 273798 570990 069260 619182 675414 989760 277846 601261 732481 893945 472855 636321 951467 523172 766089 > 4¹⁶³ [i]