MinT - Best Known (220−115, 220, s)-Nets in Base 4

Best Known (220−115, 220, s)-Nets in Base 4

(220−115, 220, 130)-Net over F₄ — Constructive and digital

Digital (105, 220, 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]

(220−115, 220, 144)-Net over F₄ — Digital

Digital (105, 220, 144)-net over F₄, using

t-expansion [i] based on digital (91, 220, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(220−115, 220, 1467)-Net in Base 4 — Upper bound on s

There is no (105, 220, 1468)-net in base 4, because

1 times m-reduction [i] would yield (105, 219, 1468)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 728992 394253 830427 650539 715949 517803 425213 168715 087826 913119 830262 236242 114453 585043 379488 459580 881877 056363 123738 333359 752751 706925 > 4²¹⁹ [i]