MinT - Best Known (163−88, 163, s)-Nets in Base 4

Best Known (163−88, 163, s)-Nets in Base 4

(163−88, 163, 104)-Net over F₄ — Constructive and digital

Digital (75, 163, 104)-net over F₄, using

t-expansion [i] based on digital (73, 163, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(163−88, 163, 112)-Net over F₄ — Digital

Digital (75, 163, 112)-net over F₄, using

t-expansion [i] based on digital (73, 163, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(163−88, 163, 941)-Net in Base 4 — Upper bound on s

There is no (75, 163, 942)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 137 113610 547560 081991 827562 279073 004451 866575 869800 237262 467686 900132 156847 403472 452950 121118 991185 > 4¹⁶³ [i]