MinT - Best Known (105, 200, s)-Nets in Base 4

Best Known (105, 200, s)-Nets in Base 4

(105, 200, 130)-Net over F₄ — Constructive and digital

Digital (105, 200, 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]

(105, 200, 169)-Net over F₄ — Digital

Digital (105, 200, 169)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 200, 2129)-Net in Base 4 — Upper bound on s

There is no (105, 200, 2130)-net in base 4, because

1 times m-reduction [i] would yield (105, 199, 2130)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 646594 436788 353317 778966 681447 064715 596025 196899 479522 750372 361068 917868 359769 059637 651473 754390 941019 146373 060773 392464 > 4¹⁹⁹ [i]