MinT - Best Known (231−76, 231, s)-Nets in Base 4

Best Known (231−76, 231, s)-Nets in Base 4

(231−76, 231, 240)-Net over F₄ — Constructive and digital

Digital (155, 231, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 77, 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]

(231−76, 231, 655)-Net over F₄ — Digital

Digital (155, 231, 655)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−76, 231, 22855)-Net in Base 4 — Upper bound on s

There is no (155, 231, 22856)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 928139 344963 965269 018782 683560 369340 583259 426385 539241 646737 238811 830889 685064 361171 423610 231336 274538 592595 759303 720326 310024 148826 943490 > 4²³¹ [i]