MinT - Best Known (250−119, 250, s)-Nets in Base 4

Best Known (250−119, 250, s)-Nets in Base 4

(250−119, 250, 130)-Net over F₄ — Constructive and digital

Digital (131, 250, 130)-net over F₄, using

t-expansion [i] based on digital (105, 250, 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]

(250−119, 250, 205)-Net over F₄ — Digital

Digital (131, 250, 205)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−119, 250, 2594)-Net in Base 4 — Upper bound on s

There is no (131, 250, 2595)-net in base 4, because

1 times m-reduction [i] would yield (131, 249, 2595)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 822314 666662 262376 699267 317350 703212 088993 104223 333050 480978 176679 504503 669190 478201 940643 461627 672277 204728 837743 744111 210711 790636 620342 188775 299840 > 4²⁴⁹ [i]