MinT - Best Known (139−42, 139, s)-Nets in Base 4

Best Known (139−42, 139, s)-Nets in Base 4

(139−42, 139, 312)-Net over F₄ — Constructive and digital

Digital (97, 139, 312)-net over F₄, using

2 times m-reduction [i] based on 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]

(139−42, 139, 600)-Net over F₄ — Digital

Digital (97, 139, 600)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−42, 139, 27936)-Net in Base 4 — Upper bound on s

There is no (97, 139, 27937)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 485874 729769 829784 509597 443175 001360 425358 781489 598767 288990 686900 095150 162323 246912 > 4¹³⁹ [i]