MinT - Best Known (60, 60+143, s)-Nets in Base 4

Best Known (60, 60+143, s)-Nets in Base 4

(60, 60+143, 66)-Net over F₄ — Constructive and digital

Digital (60, 203, 66)-net over F₄, using

t-expansion [i] based on digital (49, 203, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(60, 60+143, 91)-Net over F₄ — Digital

Digital (60, 203, 91)-net over F₄, using

t-expansion [i] based on digital (50, 203, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(60, 60+143, 413)-Net in Base 4 — Upper bound on s

There is no (60, 203, 414)-net in base 4, because

1 times m-reduction [i] would yield (60, 202, 414)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46 517744 088085 730819 027094 045118 281134 111205 118753 056592 864923 351467 459089 890617 258305 440420 407203 495397 760163 784434 638760 > 4²⁰² [i]