MinT - Best Known (72, 72+34, s)-Nets in Base 4

Best Known (72, 72+34, s)-Nets in Base 4

(72, 72+34, 240)-Net over F₄ — Constructive and digital

Digital (72, 106, 240)-net over F₄, using

4¹ times duplication [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]

(72, 72+34, 381)-Net over F₄ — Digital

Digital (72, 106, 381)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+34, 13564)-Net in Base 4 — Upper bound on s

There is no (72, 106, 13565)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6585 080357 851566 476100 680840 523326 981251 499011 217674 372360 414600 > 4¹⁰⁶ [i]