MinT - Best Known (240−109, 240, s)-Nets in Base 4

Best Known (240−109, 240, s)-Nets in Base 4

(240−109, 240, 130)-Net over F₄ — Constructive and digital

Digital (131, 240, 130)-net over F₄, using

t-expansion [i] based on digital (105, 240, 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]

(240−109, 240, 229)-Net over F₄ — Digital

Digital (131, 240, 229)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−109, 240, 3184)-Net in Base 4 — Upper bound on s

There is no (131, 240, 3185)-net in base 4, because

1 times m-reduction [i] would yield (131, 239, 3185)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 781348 123960 866587 040922 982035 558428 487478 870765 104035 756418 272989 560264 223045 291976 429890 266578 262696 716124 324658 561080 905623 056947 525155 410528 > 4²³⁹ [i]