MinT - Best Known (88, 88+62, s)-Nets in Base 5

Best Known (88, 88+62, s)-Nets in Base 5

(88, 88+62, 252)-Net over F₅ — Constructive and digital

Digital (88, 150, 252)-net over F₅, using

t-expansion [i] based on digital (85, 150, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 75, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(88, 88+62, 284)-Net over F₅ — Digital

Digital (88, 150, 284)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+62, 7460)-Net in Base 5 — Upper bound on s

There is no (88, 150, 7461)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 702 248611 354381 533798 243143 530590 373904 768926 324464 905120 897351 729001 824694 783897 266402 735809 104688 298525 > 5¹⁵⁰ [i]