MinT - Best Known (240−107, 240, s)-Nets in Base 4

Best Known (240−107, 240, s)-Nets in Base 4

(240−107, 240, 130)-Net over F₄ — Constructive and digital

Digital (133, 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]

(240−107, 240, 242)-Net over F₄ — Digital

Digital (133, 240, 242)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−107, 240, 3517)-Net in Base 4 — Upper bound on s

There is no (133, 240, 3518)-net in base 4, because

1 times m-reduction [i] would yield (133, 239, 3518)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 781287 185157 032132 297186 053811 458871 768571 260633 986844 922368 050581 239541 365284 574938 362666 873074 205195 782336 675927 984290 831657 479232 932789 792535 > 4²³⁹ [i]