MinT - Best Known (128, 128+60, s)-Nets in Base 4

Best Known (128, 128+60, s)-Nets in Base 4

(128, 128+60, 240)-Net over F₄ — Constructive and digital

Digital (128, 188, 240)-net over F₄, using

t-expansion [i] based on digital (127, 188, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (127, 189, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 63, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]

(128, 128+60, 614)-Net over F₄ — Digital

Digital (128, 188, 614)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+60, 23775)-Net in Base 4 — Upper bound on s

There is no (128, 188, 23776)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 154012 044140 748560 130531 055422 328814 557038 025160 287077 246946 640330 649030 974493 361187 197415 953483 217991 604719 156403 > 4¹⁸⁸ [i]