MinT - Best Known (224−118, 224, s)-Nets in Base 4

Best Known (224−118, 224, s)-Nets in Base 4

(224−118, 224, 130)-Net over F₄ — Constructive and digital

Digital (106, 224, 130)-net over F₄, using

t-expansion [i] based on digital (105, 224, 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]

(224−118, 224, 144)-Net over F₄ — Digital

Digital (106, 224, 144)-net over F₄, using

t-expansion [i] based on digital (91, 224, 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]

(224−118, 224, 1420)-Net in Base 4 — Upper bound on s

There is no (106, 224, 1421)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 730 268852 844604 631201 884680 590810 039017 154367 787742 191625 415775 621336 687530 593164 821839 044290 136901 072412 578273 327937 612854 246483 837920 > 4²²⁴ [i]