MinT - Best Known (71, 71+32, s)-Nets in Base 4

Best Known (71, 71+32, s)-Nets in Base 4

(71, 71+32, 240)-Net over F₄ — Constructive and digital

Digital (71, 103, 240)-net over F₄, using

2 times m-reduction [i] based on digital (71, 105, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 35, 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]

(71, 71+32, 427)-Net over F₄ — Digital

Digital (71, 103, 427)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+32, 17015)-Net in Base 4 — Upper bound on s

There is no (71, 103, 17016)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 102 867282 853269 193169 784490 613410 313863 317539 279479 212526 428103 > 4¹⁰³ [i]