MinT - Best Known (242−119, 242, s)-Nets in Base 4

Best Known (242−119, 242, s)-Nets in Base 4

(242−119, 242, 130)-Net over F₄ — Constructive and digital

Digital (123, 242, 130)-net over F₄, using

t-expansion [i] based on digital (105, 242, 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]

(242−119, 242, 179)-Net over F₄ — Digital

Digital (123, 242, 179)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−119, 242, 2141)-Net in Base 4 — Upper bound on s

There is no (123, 242, 2142)-net in base 4, because

1 times m-reduction [i] would yield (123, 241, 2142)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 512780 775751 568959 343787 294267 807193 688970 892587 403041 344469 483282 288985 085049 736258 558217 085613 789763 174759 792046 870393 653470 056594 740640 618052 > 4²⁴¹ [i]