MinT - Best Known (117, 218, s)-Nets in Base 4

Best Known (117, 218, s)-Nets in Base 4

(117, 218, 130)-Net over F₄ — Constructive and digital

Digital (117, 218, 130)-net over F₄, using

t-expansion [i] based on digital (105, 218, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(117, 218, 197)-Net over F₄ — Digital

Digital (117, 218, 197)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 218, 2622)-Net in Base 4 — Upper bound on s

There is no (117, 218, 2623)-net in base 4, because

1 times m-reduction [i] would yield (117, 217, 2623)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 44574 792027 869059 335098 369421 055527 899454 058839 348515 863379 696828 247823 966264 326687 450372 638446 928833 477025 644822 520400 557774 534941 > 4²¹⁷ [i]