MinT - Best Known (141−44, 141, s)-Nets in Base 4

Best Known (141−44, 141, s)-Nets in Base 4

(141−44, 141, 312)-Net over F₄ — Constructive and digital

Digital (97, 141, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 47, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(141−44, 141, 530)-Net over F₄ — Digital

Digital (97, 141, 530)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−44, 141, 21778)-Net in Base 4 — Upper bound on s

There is no (97, 141, 21779)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 772369 136882 593698 639105 750158 613870 749831 401263 184068 481520 058023 764851 419371 026240 > 4¹⁴¹ [i]