MinT - Best Known (243−117, 243, s)-Nets in Base 4

Best Known (243−117, 243, s)-Nets in Base 4

(243−117, 243, 130)-Net over F₄ — Constructive and digital

Digital (126, 243, 130)-net over F₄, using

t-expansion [i] based on digital (105, 243, 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]

(243−117, 243, 192)-Net over F₄ — Digital

Digital (126, 243, 192)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−117, 243, 2385)-Net in Base 4 — Upper bound on s

There is no (126, 243, 2386)-net in base 4, because

1 times m-reduction [i] would yield (126, 242, 2386)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50 471715 116847 906135 971771 417675 603547 517911 410223 614379 446775 751802 013497 569083 067694 220158 393615 663119 960532 754003 061564 488664 362826 905713 024800 > 4²⁴² [i]