MinT - Best Known (126, 126+61, s)-Nets in Base 4

Best Known (126, 126+61, s)-Nets in Base 4

(126, 126+61, 240)-Net over F₄ — Constructive and digital

Digital (126, 187, 240)-net over F₄, using

4¹ times duplication [i] based on digital (125, 186, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 62, 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]

(126, 126+61, 562)-Net over F₄ — Digital

Digital (126, 187, 562)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+61, 21674)-Net in Base 4 — Upper bound on s

There is no (126, 187, 21675)-net in base 4, because

1 times m-reduction [i] would yield (126, 186, 21675)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9626 379813 244598 854710 445934 605646 989712 964049 866258 579531 394165 486313 546674 475815 858016 923551 993157 543371 669112 > 4¹⁸⁶ [i]