MinT - Best Known (148−48, 148, s)-Nets in Base 4

Best Known (148−48, 148, s)-Nets in Base 4

(148−48, 148, 240)-Net over F₄ — Constructive and digital

Digital (100, 148, 240)-net over F₄, using

4¹ times duplication [i] based on digital (99, 147, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 49, 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]

(148−48, 148, 473)-Net over F₄ — Digital

Digital (100, 148, 473)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−48, 148, 16843)-Net in Base 4 — Upper bound on s

There is no (100, 148, 16844)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127333 969910 058494 759170 997937 047600 115351 484943 661972 831480 964259 870642 884834 787223 643756 > 4¹⁴⁸ [i]