MinT - Best Known (247−117, 247, s)-Nets in Base 4

Best Known (247−117, 247, s)-Nets in Base 4

(247−117, 247, 130)-Net over F₄ — Constructive and digital

Digital (130, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 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]

(247−117, 247, 205)-Net over F₄ — Digital

Digital (130, 247, 205)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−117, 247, 2629)-Net in Base 4 — Upper bound on s

There is no (130, 247, 2630)-net in base 4, because

1 times m-reduction [i] would yield (130, 246, 2630)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12890 290794 653475 553365 086570 440933 675146 890254 446610 038229 761470 627989 723355 682615 946471 285143 684472 758539 995549 602469 439471 137809 013173 383494 570864 > 4²⁴⁶ [i]