MinT - Best Known (232−117, 232, s)-Nets in Base 4

Best Known (232−117, 232, s)-Nets in Base 4

(232−117, 232, 130)-Net over F₄ — Constructive and digital

Digital (115, 232, 130)-net over F₄, using

t-expansion [i] based on digital (105, 232, 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]

(232−117, 232, 168)-Net over F₄ — Digital

Digital (115, 232, 168)-net over F₄, using

net from sequence [i] based on digital (115, 167)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(232−117, 232, 1823)-Net in Base 4 — Upper bound on s

There is no (115, 232, 1824)-net in base 4, because

1 times m-reduction [i] would yield (115, 231, 1824)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 222268 950862 308041 368765 663309 377713 256421 747133 472759 355633 598153 100394 580756 923667 072102 084769 189866 537341 841985 163243 832845 710326 703016 > 4²³¹ [i]