MinT - Best Known (228−121, 228, s)-Nets in Base 4

Best Known (228−121, 228, s)-Nets in Base 4

(228−121, 228, 130)-Net over F₄ — Constructive and digital

Digital (107, 228, 130)-net over F₄, using

t-expansion [i] based on digital (105, 228, 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]

(228−121, 228, 144)-Net over F₄ — Digital

Digital (107, 228, 144)-net over F₄, using

t-expansion [i] based on digital (91, 228, 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]

(228−121, 228, 1416)-Net in Base 4 — Upper bound on s

There is no (107, 228, 1417)-net in base 4, because

1 times m-reduction [i] would yield (107, 227, 1417)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47083 829668 590759 528805 874916 299059 916140 593567 204539 731331 635518 750011 216229 265903 759585 926505 390569 900483 923681 027225 660914 495819 225120 > 4²²⁷ [i]