MinT - Best Known (53, 101, s)-Nets in Base 4

Best Known (53, 101, s)-Nets in Base 4

(53, 101, 66)-Net over F₄ — Constructive and digital

Digital (53, 101, 66)-net over F₄, using

t-expansion [i] based on digital (49, 101, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(53, 101, 95)-Net over F₄ — Digital

Digital (53, 101, 95)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 101, 1097)-Net in Base 4 — Upper bound on s

There is no (53, 101, 1098)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 530286 297438 030354 492327 693136 869434 926437 406641 861885 352996 > 4¹⁰¹ [i]