MinT - Best Known (123, 123+59, s)-Nets in Base 4

Best Known (123, 123+59, s)-Nets in Base 4

(123, 123+59, 240)-Net over F₄ — Constructive and digital

Digital (123, 182, 240)-net over F₄, using

1 times m-reduction [i] based on digital (123, 183, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 61, 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]

(123, 123+59, 563)-Net over F₄ — Digital

Digital (123, 182, 563)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+59, 22244)-Net in Base 4 — Upper bound on s

There is no (123, 182, 22245)-net in base 4, because

1 times m-reduction [i] would yield (123, 181, 22245)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 399490 606170 786581 358297 050772 609551 843814 330162 867494 189793 609470 616752 183864 209675 210658 718103 429492 681936 > 4¹⁸¹ [i]