MinT - Best Known (147−44, 147, s)-Nets in Base 4

Best Known (147−44, 147, s)-Nets in Base 4

(147−44, 147, 384)-Net over F₄ — Constructive and digital

Digital (103, 147, 384)-net over F₄, using

trace code for nets [i] based on digital (5, 49, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(147−44, 147, 652)-Net over F₄ — Digital

Digital (103, 147, 652)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−44, 147, 31793)-Net in Base 4 — Upper bound on s

There is no (103, 147, 31794)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31831 068594 535865 740074 546080 439730 599390 051780 270202 399920 810067 953520 860713 450605 951120 > 4¹⁴⁷ [i]