MinT - Best Known (221−115, 221, s)-Nets in Base 4

Best Known (221−115, 221, s)-Nets in Base 4

(221−115, 221, 130)-Net over F₄ — Constructive and digital

Digital (106, 221, 130)-net over F₄, using

t-expansion [i] based on digital (105, 221, 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]

(221−115, 221, 144)-Net over F₄ — Digital

Digital (106, 221, 144)-net over F₄, using

t-expansion [i] based on digital (91, 221, 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]

(221−115, 221, 1504)-Net in Base 4 — Upper bound on s

There is no (106, 221, 1505)-net in base 4, because

1 times m-reduction [i] would yield (106, 220, 1505)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 887021 733793 077577 741875 211792 185652 414122 985654 110849 621371 628930 411379 973556 108337 387698 562563 909348 045083 452824 883242 198611 404064 > 4²²⁰ [i]