MinT - Best Known (225−74, 225, s)-Nets in Base 4

Best Known (225−74, 225, s)-Nets in Base 4

(225−74, 225, 240)-Net over F₄ — Constructive and digital

Digital (151, 225, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 75, 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]

(225−74, 225, 641)-Net over F₄ — Digital

Digital (151, 225, 641)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−74, 225, 22355)-Net in Base 4 — Upper bound on s

There is no (151, 225, 22356)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2911 440962 076350 009719 864220 200922 508089 733596 796659 315794 931376 865478 033808 724123 447273 261250 078832 972084 346324 023053 622014 654761 677400 > 4²²⁵ [i]