MinT - Best Known (148−45, 148, s)-Nets in Base 4

Best Known (148−45, 148, s)-Nets in Base 4

(148−45, 148, 312)-Net over F₄ — Constructive and digital

Digital (103, 148, 312)-net over F₄, using

2 times m-reduction [i] based on digital (103, 150, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 50, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(148−45, 148, 613)-Net over F₄ — Digital

Digital (103, 148, 613)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−45, 148, 31793)-Net in Base 4 — Upper bound on s

There is no (103, 148, 31794)-net in base 4, because

1 times m-reduction [i] would yield (103, 147, 31794)-net in base 4, but
- 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]