MinT - Best Known (163−53, 163, s)-Nets in Base 4

Best Known (163−53, 163, s)-Nets in Base 4

(163−53, 163, 240)-Net over F₄ — Constructive and digital

Digital (110, 163, 240)-net over F₄, using

4¹ times duplication [i] based on digital (109, 162, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 54, 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]

(163−53, 163, 507)-Net over F₄ — Digital

Digital (110, 163, 507)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−53, 163, 19815)-Net in Base 4 — Upper bound on s

There is no (110, 163, 19816)-net in base 4, because

1 times m-reduction [i] would yield (110, 162, 19816)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34 197892 537005 688842 326010 986095 553909 884966 238730 925614 497352 441552 775992 140227 441886 394178 910620 > 4¹⁶² [i]