MinT - Best Known (144−47, 144, s)-Nets in Base 4

Best Known (144−47, 144, s)-Nets in Base 4

(144−47, 144, 240)-Net over F₄ — Constructive and digital

Digital (97, 144, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 48, 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]

(144−47, 144, 451)-Net over F₄ — Digital

Digital (97, 144, 451)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−47, 144, 17382)-Net in Base 4 — Upper bound on s

There is no (97, 144, 17383)-net in base 4, because

1 times m-reduction [i] would yield (97, 143, 17383)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 124 416918 718596 545456 381903 774643 674507 545053 235620 940849 346665 201561 680524 266182 998680 > 4¹⁴³ [i]