MinT - Best Known (245−111, 245, s)-Nets in Base 4

Best Known (245−111, 245, s)-Nets in Base 4

(245−111, 245, 130)-Net over F₄ — Constructive and digital

Digital (134, 245, 130)-net over F₄, using

t-expansion [i] based on digital (105, 245, 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]

(245−111, 245, 235)-Net over F₄ — Digital

Digital (134, 245, 235)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−111, 245, 3289)-Net in Base 4 — Upper bound on s

There is no (134, 245, 3290)-net in base 4, because

1 times m-reduction [i] would yield (134, 244, 3290)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 810 907279 019184 277523 845558 894190 088384 715048 599475 274890 144425 077627 823649 880134 268673 386497 572786 625582 342481 278888 290993 869376 377704 297525 134520 > 4²⁴⁴ [i]