MinT - Best Known (151, 151+73, s)-Nets in Base 4

Best Known (151, 151+73, s)-Nets in Base 4

(151, 151+73, 240)-Net over F₄ — Constructive and digital

Digital (151, 224, 240)-net over F₄, using

1 times m-reduction [i] based on 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]

(151, 151+73, 660)-Net over F₄ — Digital

Digital (151, 224, 660)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+73, 25500)-Net in Base 4 — Upper bound on s

There is no (151, 224, 25501)-net in base 4, because

1 times m-reduction [i] would yield (151, 223, 25501)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 181 952298 336368 508063 823964 726072 766829 087017 656482 164690 141499 669430 044012 447630 475624 643523 914932 107477 017914 809375 861700 868762 833236 > 4²²³ [i]