MinT - Best Known (219−105, 219, s)-Nets in Base 4

Best Known (219−105, 219, s)-Nets in Base 4

(219−105, 219, 130)-Net over F₄ — Constructive and digital

Digital (114, 219, 130)-net over F₄, using

t-expansion [i] based on digital (105, 219, 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]

(219−105, 219, 178)-Net over F₄ — Digital

Digital (114, 219, 178)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−105, 219, 2210)-Net in Base 4 — Upper bound on s

There is no (114, 219, 2211)-net in base 4, because

1 times m-reduction [i] would yield (114, 218, 2211)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 178854 836901 886472 447498 670788 372495 304376 155692 510589 437223 270570 054179 428642 108461 163598 711187 031078 461062 544398 708774 545140 435040 > 4²¹⁸ [i]