MinT - Best Known (61, 61+29, s)-Nets in Base 4

Best Known (61, 61+29, s)-Nets in Base 4

(61, 61+29, 240)-Net over F₄ — Constructive and digital

Digital (61, 90, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 30, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(61, 61+29, 333)-Net over F₄ — Digital

Digital (61, 90, 333)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+29, 13531)-Net in Base 4 — Upper bound on s

There is no (61, 90, 13532)-net in base 4, because

1 times m-reduction [i] would yield (61, 89, 13532)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 383151 674224 454542 431950 577840 131926 542390 685982 793580 > 4⁸⁹ [i]